6x^4-48x^2+72=0

Solution for 6x^4-48x^2+72=0 equation:

Simplifying
6x4 + -48x2 + 72 = 0

Reorder the terms:
72 + -48x2 + 6x4 = 0

Solving
72 + -48x2 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -8x2 + x4) = 0

Factor a trinomial.
6((2 + -1x2)(6 + -1x2)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {-1.414213562, 1.414213562, -2.449489743, 2.449489743}